If `P(15 ,r-1): P(16 ,r-2)=3:4` , find `rdot`

Explanation

`P(15, r-1): P(16, r-2)=3: 4`


`Rightarrow frac{15 !}{(15-r+1) !} times frac{(16-r+2) !}{16 !}=frac{3}{4}`


`Rightarrow frac{15 !}{(16-r) !} times frac{(18-r) !}{16 times 15 !}=frac{3}{4}`


`Rightarrow frac{(18-r)(17-r)(16-r) !}{(16-r) !(16)}=frac{3}{4}`


`Rightarrow(18-r)(17-r)=12`


`Rightarrow(18-r)(17-r)=4 times 3`


On comparing the LHS and the RHS in above expression, we get :


`Rightarrow 18-r=14`


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